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Interior Path Methods for Heuristic Integer Programming Procedures

Author

Listed:
  • Bruce H. Faaland

    (University of Washington, Seattle, Washington)

  • Frederick S. Hillier

    (Stanford University, Stanford, California)

Abstract

This paper considers heuristic procedures for general mixed integer linear programming with inequality constraints. It focuses on the question of how to most effectively initialize such procedures by constructing an “interior path” from which to search for good feasible solutions. These paths lead from an optimal solution for the corresponding linear programming problem (i.e., deleting integrality restrictions) into the interior of the feasible region for this problem. Previous methods for constructing linear paths of this kind are analyzed from a statistical viewpoint, which motivates a promising new method. These methods are then extended to piecewise linear paths in order to improve the direction of search in certain cases where constraints that are not binding on the optimal linear programming solution become particularly relevant. Computational experience is reported.

Suggested Citation

  • Bruce H. Faaland & Frederick S. Hillier, 1979. "Interior Path Methods for Heuristic Integer Programming Procedures," Operations Research, INFORMS, vol. 27(6), pages 1069-1087, December.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:6:p:1069-1087
    DOI: 10.1287/opre.27.6.1069
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    Cited by:

    1. Egon Balas & Sebastián Ceria & Milind Dawande & Francois Margot & Gábor Pataki, 2001. "Octane: A New Heuristic for Pure 0--1 Programs," Operations Research, INFORMS, vol. 49(2), pages 207-225, April.
    2. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.

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